Well, it's a probabilistic argument. While it's possible that it's just a coincidence that we both have qualia and discuss qualia, it's an extremely unlikely coincidence.
To twist your movie analogy beyond all use, it's like trying on some clothes in a dressing room, then watching a movie with a scene that features you trying on those exact same clothes in that exact same dressing room in the exact same way you tried them on. It's possible that the filmmaker just happened to capture the exact same scene by chance, but it's vastly more likely that he was secretly recording you.
i would argue that we can't accurately infer any likelihood without knowing what the entire probability space is. in the dressing-room example, we are assuming there are not many, many dressing rooms that look similar, and many, many people that look just like us, and many different sets of the same clothes. but that is just an assumption. we have no idea about the probability space of different material universes and how qualia is embedded in them.
To twist your movie analogy beyond all use, it's like trying on some clothes in a dressing room, then watching a movie with a scene that features you trying on those exact same clothes in that exact same dressing room in the exact same way you tried them on. It's possible that the filmmaker just happened to capture the exact same scene by chance, but it's vastly more likely that he was secretly recording you.